A novel structure preserving scheme for Schrondiger-Poisson systems.
- Dr. Th. Katsaounis
B2 L5 R5220
In this talk I will present a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrodinger-Poisson system. We use the Crank-Nicolson scheme as a time-stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system’s mass conservation and energy balance laws for constant discretization parameters.
Overview
Abstract
Coffee time: 15:30 to 16:00
In this talk I will present a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrodinger-Poisson system. We use the Crank-Nicolson scheme as a time-stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system’s mass conservation and energy balance laws for constant discretization parameters. We conclude by presenting some numerical experiments, including an example from cosmology and an example with variable time-steps which demonstrate the effectiveness and robustness of the new scheme.
Brief Biography
Dr. Th. Katsaounis is a Professor of Mathematics at the University of Crete, Greece. He received his Ph.D in 1994 from the Univ. of Tennessee USA, in applied and computational mathematics. After his postdoctoral studies in the Ecole Normale Superieure of Paris, he joined the Dept. of Applied Mathematics of Univ. of Crete, Greece as an Assistant professor in 2003. Dr. Th. Katsaounis was a Research Scientist at KAUST from 2015 to 2020. His research interests are in the area of mathematical modelling and numerical solution of pde's arising as models in various applications.
